Willpower apparently can be bought. The chance to win or lose $20 a month enticed dieters in a yearlong study to drop an average of 9 pounds.

Many employers, insurers and Internet programs dangle dollars to try to change bad habits like smoking or not exercising, but most studies have found this doesn’t work very well or for very long.

The study, done with Mayo Clinic employees, was the longest test yet of financial incentives for weight loss. Doctors think it succeeded because it had a mix of carrots and sticks and penalties for not losing weight, multiple ways to earn cash for succeeding, and a chance to recoup lost money if you fell off the “diet wagon” and later repented.